5.1 Quadratic function & Standard form-y=ax²+bx+c Parabola- the graph of a quadratic function is U-Shaped Vertex- The lowest point on the graph of a quadratic function Axis of Symmetry- the vertical line through the vertex
5.2 Binomials- have two terms
Ex) x+3 Trinomial- have three terms
Ex) x²+8x+15 Factoring- Can be used to turn a Trinomal into a Binomial Monomial- an expression that has only one term Quadratic equation & standard form- ax²+bx+c=0 Zeros- The numbers p and q are called zeros in the equation y=a(x-p)(x-q)
5.3 Square root- A number r is square root of a number s if r² =s Radical sign-√ Radicand- the number beneath the radical sign Radical- the expression √s Rationalizing the denominator- eliminating the square root in the denominator by multiplying both the numerator and the denominator by the denominator
5.4 Imaginary Unit-i√-1 & i²=-1 Complex number & standard form-a+bi Imaginary Number- If b≠0 Pure imaginary number- If a=0 and b≠0 Complex Plane- every complex number corresponds to a point on this plane
5.5 Completing the square- process that allows you to write an expression of the form x²+bx as the square binomial
5.6 Quadratic formula
x = -b±√b²-4ac / 2a Discriminat-b²-4ac
5.7 Quadratic inequalities in two variables- y<ax²+bx+c, y<ax²+bx+c, y>ax²+bx+c, y>ax²+bx+c, Quadratic inequalities in one variables- ax²+bx+c<0, ax²+bx+c<0, ax²+bx+c>0, ax²+bx+c>0,
5.8 Vertex Form- y=a(x-h)²+k Intercept Form- y=a(x-p)(x-q) Quadratic Model- a quadratic function that represents a real data set
An Intro to Quadratics
Solving Quadratic Equations by Factoring
Completing the Square ABRA KADABRA!! This guy has fast (and neat) handwriting
You can check you answers in the back of your text book on page SA16 (# 33, 51, 45, 67, 79) .
5.3
Simplify the expression
1.)
radical symbol
2 7 *
radical symbol
7 2.)
radical symbol
75/36
Solve the Equation
1.) 3x2 = 108 2.)2 (a-6) 2 – 45 = 53
Check Answers with the back of you textbook on page SA17 (#27, 41, 53, 65)
5.4
Solve the equation
1.)3x2 = -81 2.)–1/8 (v +3) 2 = 7 Plot the numbers on the same complex plane. 1.)4 + 2 i Write the expression as a complex number in standard form. 1.)(2 + 3 i) + (7 + i) 2.)(- .4 + .9 i) - (- .6 + i)
3.) (-4 + 2 i) (11 – 7)
4.) (15 - 8 i) 2 5.) 3 +
radical symbol
i
3 –
radical symbol
i 6.) 6 - i2
6 + i 2
Find the absolute value of the complex number. 1.)4 - 8 i
Check Answers with the back of you textbook on page SA18 (#25, 31, 49, 57, 73, 81)
5.5 Write the expression as the square of a binomial. 1.)x2 – 24x + 144
2.)x2 - 4/9x + 4/81 Solve the equation by completing the square 1.)x2 + 20x + 104 =0
2.)x2 + 84x + 300 =0 Write the quadratic function in vertex form and Identify the vertex. 1.)y = x2 - 6x + 11 2.)y = 3x2 - 12x + 1
Check Answers with the back of you textbook on page SA18 (#25, 31, 49, 57, 73, 81)
5.6 Use the quadratic formula to solve the equation. 1.)x2 - 5x – 14 =0 2.) 40x - 7x2 = 101 - 3x2 Solve using factoring, finding square roots, and quadratic terms. 2.)x2 - 5x – 14 =0 Find the discriminate of the quadratic equation and give the number and type of solutions of equation. 1..) x2 + 3x – 6 = 0 3.)s2
radical symbol
5 + s +
radical symbol
5 = 0
Check Answers with the back of you textbook on page SA18 (#17, 43, 49, 57, & 63)
5.7 Graph the system of inequalities. 1.) y > x2 – 6x + 9 2.) y < -x2 + 6x – 3 Solve by graphing. 1.).3x2 + 24x > -41 Solve algebraically. 1.)2x2 - 4x - 5 > 0
Check Answers with the back of you textbook on page SA18 (#31, 39, & 49)
5.8 Write the quadratic function in vertex form for the parabola.
1.) whose points go through (0, 2) (4, 2)
and a vertex of (2, -2)
Write the quadratic function in intercept form for the parabola. 1.) Whose points go through (-2, 0) (1, 0)
and a vertex of (-1, -6)
Write the quadratic function in standard form whose graph passes through the given points. 1.)(1 , 2) (3 , 4 ) (6 , –5 )
2.) (-6 , 46) (2 , 14) (4 , 56)
Check Answers with the back of you textbook on page SA18 (#7, 17, 29, &33)
CAREER APPLICATION Civil engineers design and build roads, bridges, buildings, and transit systems. Civil engineers use their knowledge of geometry, trigonometry and calculus to solve problems related to their work. Engineers, in general, apply mathematics and science to research, design, and develop a wide variety of products. This is often done by taking some scientific discovery and giving it a practical application. Engineers may also use their knowledge to improve existing things, such as the efficiency or quality of a product.
5.1
Quadratic function & Standard form- y=ax²+bx+c
Parabola- the graph of a quadratic function is U-Shaped
Vertex- The lowest point on the graph of a quadratic function
Axis of Symmetry- the vertical line through the vertex
5.2
Binomials- have two terms
Ex) x+3
Trinomial- have three terms
Ex) x² +8x+15
Factoring- Can be used to turn a Trinomal into a Binomial
Monomial- an expression that has only one term
Quadratic equation & standard form- ax² +bx+c=0
Zeros- The numbers p and q are called zeros in the equation y=a(x-p)(x-q)
5.3
Square root- A number r is square root of a number s if r² =s
Radical sign- √
Radicand- the number beneath the radical sign
Radical- the expression √s
Rationalizing the denominator- eliminating the square root in the denominator by multiplying both the numerator and the denominator by the denominator
5.4
Imaginary Unit- i√-1 & i²=-1
Complex number & standard form- a+bi
Imaginary Number- If b≠0
Pure imaginary number- If a=0 and b≠0
Complex Plane- every complex number corresponds to a point on this plane
5.5
Completing the square- process that allows you to write an expression of the form x²+bx as the square binomial
5.6
Quadratic formula
x = -b ± √b²-4ac / 2a
Discriminat- b²-4ac
5.7
Quadratic inequalities in two variables- y<ax²+bx+c, y<ax²+bx+c, y>ax²+bx+c, y>ax²+bx+c,
Quadratic inequalities in one variables- ax²+bx+c<0, ax²+bx+c<0, ax²+bx+c>0, ax²+bx+c>0,
5.8
Vertex Form- y=a(x-h)²+k
Intercept Form- y=a(x-p)(x-q)
Quadratic Model- a quadratic function that represents a real data set
An Intro to Quadratics
Solving Quadratic Equations by Factoring
Completing the Square ABRA KADABRA!! This guy has fast (and neat) handwriting
5.1
Graph the quadratic equation.
1.) y = 2x2 – 12x +192.) y = - (x-2) 2 - 1
3.) y = 1/3 (x+4) (x+1)
Factor the expression.
1.) q2 – 7q –10
2.) 9s2 + 12s + 4
3.) 12y2 – 25y –7
Solve the equation.
1.) 5x2 – 13x + 6 = 0
2.) (w+6) 2 = 3(w+12) - w2
5.3
Simplify the expression
1.)2.)
Solve the Equation
1.) 3x2 = 1082.) 2 (a-6) 2 – 45 = 53
5.4
Solve the equation
1.) 3x2 = -812.) –1/8 (v +3) 2 = 7
Plot the numbers on the same complex plane.
1.) 4 + 2 i
Write the expression as a complex number in standard form.
1.) (2 + 3 i) + (7 + i)
2.) (- .4 + .9 i) - (- .6 + i)
3.) (-4 + 2 i) (11 – 7)
4.) (15 - 8 i) 2
5.) 3 +
3 –
6.) 6 - i2
6 + i 2
Find the absolute value of the complex number.
1.) 4 - 8 i
5.5
Write the expression as the square of a binomial.
1.) x2 – 24x + 144
2.) x2 - 4/9x + 4/81
Solve the equation by completing the square
1.) x2 + 20x + 104 =0
2.) x2 + 84x + 300 =0
Write the quadratic function in vertex form and Identify the vertex.
1.) y = x2 - 6x + 11
2.) y = 3x2 - 12x + 1
Use the quadratic formula to solve the equation.
1.) x2 - 5x – 14 =0
2.) 40x - 7x2 = 101 - 3x2
Solve using factoring, finding square roots, and quadratic terms.
2.) x2 - 5x – 14 =0
Find the discriminate of the quadratic equation and give the number and type of solutions of equation.
1..) x2 + 3x – 6 = 0
3.) s2
5.7
Graph the system of inequalities.
1.) y > x2 – 6x + 9
2.) y < -x2 + 6x – 3
Solve by graphing.
1.) .3x2 + 24x > -41
Solve algebraically.
1.) 2x2 - 4x - 5 > 0
Write the quadratic function in vertex form for the parabola.
1.) whose points go through (0, 2) (4, 2)
and a vertex of (2, -2)
Write the quadratic function in intercept form for the parabola.
1.) Whose points go through (-2, 0) (1, 0)
and a vertex of (-1, -6)
Write the quadratic function in standard form whose graph passes through the given points.
1.) (1 , 2) (3 , 4 ) (6 , –5 )
2.) (-6 , 46) (2 , 14) (4 , 56)
CAREER APPLICATION
Civil engineers design and build roads, bridges, buildings, and transit systems. Civil engineers use their knowledge of geometry, trigonometry and calculus to solve problems related to their work. Engineers, in general, apply mathematics and science to research, design, and develop a wide variety of products. This is often done by taking some scientific discovery and giving it a practical application. Engineers may also use their knowledge to improve existing things, such as the efficiency or quality of a product.